Hello everybody,

I'm dealing with this problem already for a couple of days and I got really stuck, I just need to understand in plain English or Spanish (lol) how to deal with this problem.

Here is the problem:

Let $\displaystyle f(n)$ be a polynomial of order $\displaystyle k$, that is $\displaystyle f(n)=b_{k}n^{k} + b_{k-1}n^{k-1} +...+ b_{0}$.

Prove that $\displaystyle f(n) = \Omega(n^{k})$.

Note: $\displaystyle b_{k} > 0$, but $\displaystyle b_{i}$ may be negative for $\displaystyle 0\le{i}<k$.

Hint: use the highest index for which $\displaystyle b_{s}< 0$.

[How can I prove that? and what is $\displaystyle b_{s}$???]